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Homework Help: Differential Geometry/notation help

  1. Apr 18, 2012 #1
    1. The problem statement, all variables and given/known data

    I have this theorem which I am having trouble understanding due to notation.

    Theorem: Define S,S'[itex]\subseteq[/itex]ℝ3 to be surfaces. Let f:S→S' be a smooth map. f is a local isometry if for all p in S, and all w1,w2 in TpS,

    The thing I don't get, is what does dfp(w1) mean?
    What action is going on between dfp and w1?

    Thank you for your time.
  2. jcsd
  3. Apr 18, 2012 #2


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    Science Advisor

    [itex]df_p[/itex] is the derived mapping from the tangent space at p in S to the tangent space at f(p) in S'.
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